The EM algorithm for graphical association models with missing data
Computational Statistics & Data Analysis - Special issue dedicated to Toma´sˇ Havra´nek
Adaptive Probabilistic Networks with Hidden Variables
Machine Learning - Special issue on learning with probabilistic representations
Robust Learning with Missing Data
Machine Learning
Exploiting Qualitative Knowledge in the Learning of Conditional Probabilities of Bayesian Networks
UAI '00 Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence
Data perturbation for escaping local maxima in learning
Eighteenth national conference on Artificial intelligence
Comprehensive Database for Facial Expression Analysis
FG '00 Proceedings of the Fourth IEEE International Conference on Automatic Face and Gesture Recognition 2000
Bayesian networks and information retrieval: an introduction to the special issue
Information Processing and Management: an International Journal - Special issue: Bayesian networks and information retrieval
Active and Dynamic Information Fusion for Facial Expression Understanding from Image Sequences
IEEE Transactions on Pattern Analysis and Machine Intelligence
Recognizing Facial Expression: Machine Learning and Application to Spontaneous Behavior
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
A Dynamic Bayesian Network Model for Autonomous 3D Reconstruction from a Single Indoor Image
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 2
Inferring Facial Action Units with Causal Relations
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 2
Operations for learning with graphical models
Journal of Artificial Intelligence Research
Challenge: what is the impact of Bayesian networks on learning?
IJCAI'97 Proceedings of the 15th international joint conference on Artifical intelligence - Volume 1
A theoretical framework for learning Bayesian networks with parameter inequality constraints
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Local learning in probabilistic networks with hidden variables
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 2
Learning Bayesian network parameters under order constraints
International Journal of Approximate Reasoning
Elicitation of probabilities for belief networks: combining qualitative and quantitative information
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Update rules for parameter estimation in Bayesian networks
UAI'97 Proceedings of the Thirteenth conference on Uncertainty in artificial intelligence
The Information bottleneck EM algorithm
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
PCOPM: a probabilistic CBR framework for obesity prescription management
ICIC'10 Proceedings of the Advanced intelligent computing theories and applications, and 6th international conference on Intelligent computing
Tutorial and selected approaches on parameter learning in bayesian network with incomplete data
ISNN'12 Proceedings of the 9th international conference on Advances in Neural Networks - Volume Part I
Incorporating expert judgement into Bayesian network machine learning
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
A Multi-Objective Evolutionary Algorithm for enhancing Bayesian Networks hybrid-based modeling
Computers & Mathematics with Applications
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Bayesian networks (BNs) have gained increasing attention in recent years. One key issue in Bayesian networks is parameter learning. When training data is incomplete or sparse or when multiple hidden nodes exist, learning parameters in Bayesian networks becomes extremely difficult. Under these circumstances, the learning algorithms are required to operate in a high-dimensional search space and they could easily get trapped among copious local maxima. This paper presents a learning algorithm to incorporate domain knowledge into the learning to regularize the otherwise ill-posed problem, to limit the search space, and to avoid local optima. Unlike the conventional approaches that typically exploit the quantitative domain knowledge such as prior probability distribution, our method systematically incorporates qualitative constraints on some of the parameters into the learning process. Specifically, the problem is formulated as a constrained optimization problem, where an objective function is defined as a combination of the likelihood function and penalty functions constructed from the qualitative domain knowledge. Then, a gradient-descent procedure is systematically integrated with the E-step and M-step of the EM algorithm, to estimate the parameters iteratively until it converges. The experiments with both synthetic data and real data for facial action recognition show our algorithm improves the accuracy of the learned BN parameters significantly over the conventional EM algorithm.